Show that in any group of hundred order that every element has order that is a power of a prime or there is an element of order 10

 By Lagrange's theorem , possible orders of elements of G are 1,2,4,5,10,20,25,50 and 100.  O(x²⁵) is 4 which is 2² O(x⁹) is 100 which is 10² 0(x⁵⁰) is 2